Question: $J$ $K$ $L$ If: $ JK = 3x + 5$, $ JL = 84$, and $ KL = 6x + 7$, Find $KL$.
From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {3x + 5} + {6x + 7} = {84}$ Combine like terms: $ 9x + 12 = {84}$ Subtract $12$ from both sides: $ 9x = 72$ Divide both sides by $9$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $KL$ $ KL = 6({8}) + 7$ Simplify: $ {KL = 48 + 7}$ Simplify to find ${KL}$ : $ {KL = 55}$